Image forming apparatus

ABSTRACT

An image forming apparatus, including: a deflection unit configured to deflect light beams emitted from light emitting points with a mirror face to form scanning lines in a second direction orthogonal to a first direction in which a photosensitive drum is rotated; a correction unit configured to correct an optical face tangle error of the mirror based on a deviation amount from a distance between the deflection unit and the photosensitive member; a calculation unit configured to calculate a positional deviation amount of the emitting points in the first direction; a transformation unit configured to transform a pixel position of an input image based on the positional deviation amount so that an interval between the scanning lines is a predetermined interval; and a filtering unit configured to obtain a pixel value of an output image based on the transformed pixel position of the input image.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to an image forming apparatus, which isconfigured to correct distortion and uneven image density of an imageduring image formation of a two-dimensional image by the image formingapparatus, e.g., a digital copying machine, a multifunctionalperipheral, or a laser printer.

Description of the Related Art

In electrophotographic image forming apparatus such as a laser printerand a copying machine, there has been generally known a configuration toform a latent image on a photosensitive member with the use of a lightscanning device configured to perform scanning with a laser beam. In thelight scanning device of a laser scanning type, a laser beam collimatedwith the use of a collimator lens is deflected by a rotary polygonmirror, and the deflected laser beam is formed into an image on aphotosensitive member with the use of an elongated fθ lens. Further,there is known multibeam scanning in which a laser light source having aplurality of light emitting points is included in one package so as toperform scanning with a plurality of laser beams simultaneously.

Meanwhile, in order to form a satisfactory image without uneven imagedensity and banding, it is desired that distances between scanning linesof which positions to be scanned with a laser beam are adjacent to eachother in a rotational direction of the photosensitive member be equal toeach other. However, the distances between the scanning lines are varieddue to a plurality of factors described below. The distances between thescanning lines on the photosensitive member are varied by, for example,a fluctuation in a surface speed of the photosensitive member, or arotation speed fluctuation of a rotary polygon mirror. Further, thedistances between the scanning lines are also varied by a variation inangle of mirror faces of the rotary polygon mirror with respect to arotary shaft of the rotary polygon mirror and a variation in intervalsbetween light emitting points arranged on a laser light source. To copewith uneven image density and banding caused by such factors, there hasbeen proposed a technology of correcting banding by controlling anexposure amount of the light scanning device. For example, in JapanesePatent Application Laid-Open No. 2012-098622, there is described aconfiguration in which a beam position detection unit configured todetect a beam position in a sub-scanning direction is arranged in thevicinity of the photosensitive member, and the exposure amount of thelight scanning device is adjusted based on scanning distance informationobtained from a detected beam position, to thereby make banding lessnoticeable.

Due to factors such as a variation in dimensions of components formingthe image forming apparatus, a laser beam emitted from a light scanningdevice has positional deviation from the position of an ideal focus in afocus depth direction. The amount of banding changes when the positionaldeviation occurs in the focus depth direction. FIG. 17A is a diagram forillustrating a state of an optical path formed based on the inclinationof a mirror face of a rotary polygon mirror. For example, as illustratedin FIG. 17A, when a photosensitive member is deviated by ±α from adistance Lf which is a predetermined distance, a positional deviation of±Δd occurs in a sub-scanning direction. As shown in FIG. 17C, the amountof optical face tangle of a just focus correction position is correctedby a lens 1001, but the amount is as shown in FIG. 17B or FIG. 17D atthe position deviated by ±α from the distance Lf. Thus, when thepositional deviation occurs in the focus depth direction, positionaldeviation is caused in the sub-scanning direction to change the amountof banding.

In the related art, when the positional deviation occurs in the focusdepth direction due to the factors such as a variation in dimensions ofcomponents, a correction residual occurs because of an error in acorrection amount. Even a configuration including a position detectionunit configured to detect the position of a light beam has a problem inthat, when the position of the position detection unit in the focusdepth direction differs from the position of the photosensitive memberin the focus depth direction due to, for example, a mounting error ofthe position detection unit, a detection error occurs, and bandingcannot be eliminated completely.

SUMMARY OF THE INVENTION

The present invention has been made under the above-mentionedcircumstances, and it is an object of the present invention to reduceuneven image density even when focus deviation of a laser beam radiatedon a photosensitive member from a light scanning device occurs due to avariation on an image forming apparatus side and a mounting error of thelight scanning device.

In order to solve the above-mentioned problem, according to oneembodiment of the present invention, there is provided an image formingapparatus, comprising:

-   -   a light source comprising a plurality of light emitting points;    -   a photosensitive member configured to rotate in a first        direction so that a latent image is formed on the photosensitive        member by light beams emitted from the light source;    -   a deflection unit configured to deflect the light beam emitted        from the light source with a mirror face and cause light spots        of the light beams radiated on the photosensitive member to be        moved in a second direction orthogonal to the first direction to        form scanning lines;    -   a storage unit configured to store information on positional        deviation of the plurality of light emitting points in the first        direction and information on an optical face tangle error of the        mirror face of the deflection unit in accordance with the second        direction;    -   a correction unit configured to correct the information on the        optical face tangle error stored in the storage unit, based on a        deviation amount from a predetermined distance between the        deflection unit and the photosensitive member;    -   a calculation unit configured to calculate a positional        deviation amount based on the information on the positional        deviation stored in the storage unit and the information on the        optical face tangle error corrected by the correction unit;    -   a transformation unit configured to transform a position of a        pixel of an input image by performing coordinate transformation        based on the positional deviation amount calculated by the        calculation unit so that an interval between the scanning lines        on the photosensitive member is a predetermined interval; and    -   a filtering unit configured to obtain a pixel value of a pixel        of an output image by subjecting a pixel value of the pixel of        the input image to a convolution operation based on the position        of the pixel of the input image after the coordinate        transformation.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a view for illustrating an entire image forming apparatus offirst and second embodiments.

FIG. 1B is a view for illustrating a configuration of the periphery of aphotosensitive drum and a light scanning device of the first embodiment.

FIG. 2 is a block diagram of the image forming apparatus of the firstand second embodiments.

FIG. 3 is a diagram for illustrating positional deviation of scanninglines of the first and second embodiments.

FIG. 4 is a block diagram for illustrating a step of storing informationin a memory of the first and second embodiments.

FIG. 5 is a time chart for illustrating one scanning period of the firstand second embodiments.

FIG. 6 is a flowchart for illustrating image forming processing of thefirst and second embodiments.

FIG. 7 is a flowchart for illustrating correction processing of thefirst and second embodiments.

FIG. 8A, FIG. 8B, FIG. 8C, and FIG. 8D are each a diagram forillustrating positional deviation of pixels for each classification ofthe first and second embodiments.

FIG. 9A and FIG. 9B are each a graph for showing coordinatetransformation of pixel positions in a sub-scanning direction of thefirst and second embodiments.

FIG. 10A, FIG. 10B, FIG. 10C, and FIG. 10D are each a graph for showingcoordinate transformation of pixel positions in the sub-scanningdirection of the first and second embodiments.

FIG. 11A and FIG. 11B are each a graph for showing coordinatetransformation of pixel positions in the sub-scanning direction of thefirst and second embodiments.

FIG. 12A, FIG. 12B, and FIG. 12C are each a graph for showing aconvolution function to be used in filtering of the first and secondembodiments.

FIG. 12D is a graph for showing a correction value and a coefficient.

FIG. 13A, FIG. 13B, FIG. 13C, and FIG. 13D are each a diagram forillustrating the filtering for each classification of positionaldeviation of the first and second embodiments.

FIG. 14 is a flowchart for illustrating the filtering of the first andsecond embodiments.

FIG. 15A, FIG. 15B, FIG. 15C, and FIG. 15D are each a test chart of thefirst embodiment.

FIG. 16A and FIG. 16B are each a graph for showing a relationshipbetween an amplitude gain and an amount of optical face tangle of thesecond embodiment.

FIG. 16C is a graph for showing a relationship between an amplitude gainand focus distance information.

FIG. 17A, FIG. 17B, FIG. 17C, and FIG. 17D are each a diagram forshowing a relationship between a mirror face of a rotary polygon mirrorand an amount of optical face tangle thereof of the related art.

FIG. 18 is a diagram for showing a conversion table for converting imagedata (density data) into drive data for generating a PWM signal.

DESCRIPTION OF THE EMBODIMENTS

The embodiments will be described in detail below in an illustrativemanner with reference to the drawings. A direction of an axis ofrotation of a photosensitive drum, which is a direction in whichscanning is performed with a laser beam, is defined as a main scanningdirection which is a second direction, and a rotational direction of thephotosensitive drum, which is a direction substantially orthogonal tothe main scanning direction, is defined as a sub-scanning directionwhich is a first direction.

<Change in Amount of Banding Caused by Positional Deviation in FocusDepth Direction>

A relationship between the above-mentioned positional deviation in thefocus depth direction and banding will be described in detail. Due tofactors such as a variation in dimensions of components forming an imageforming apparatus, a laser beam emitted from a light scanning device haspositional deviation from the position of an ideal focus in the focusdepth direction. The amount of banding changes when the positionaldeviation occurs in the focus depth direction. A relationship betweenthe positional deviation in the focus depth direction and the bandingwill be described later. FIG. 17A is a diagram for illustrating a stateof an optical path formed based on the inclination of a mirror face(reflection face) of a rotary polygon mirror. FIG. 17A is a diagram forillustrating a photosensitive drum 102 of FIG. 1B described later whenviewed from a rotation axis direction. Based on the state in which themirror face of the rotary polygon mirror forms an ideal angle, theoptical path of a laser beam reflected from a mirror face 1002 a of therotary polygon mirror in the ideal state is represented by an opticalpath B in FIG. 17A. The laser beam reflected from a mirror face 1002 bof the rotary polygon mirror which is inclined from the ideal angle andhas an optical face tangle error is radiated on a photosensitive memberthrough an optical path A at a different position from that of theoptical path B. In general, in order to address the deviation of theoptical path caused by the optical face tangle error of the mirror faceof the rotary polygon mirror, an optical correction lens 1001 configuredto correct an optical face tangle error by optically adjusting theposition of an optical path is arranged. When the lens 1001 is arranged,the positional deviation caused by an optical face tangle error can becorrected at an ideal focus position (sometimes referred to as “justfocus correction position).

In the example of FIG. 17A, when the photosensitive member is located ata position of the distance Lf based on the mirror face 1002 a of therotary polygon mirror in the ideal state, the optical path A iscorrected by the lens 1001 to eliminate positional deviation. The lens1001 corrects the optical path A of the laser beam reflected from themirror face 1002 b of the rotary polygon mirror which has an opticalface tangle error, and corrects the positional deviation caused by anoptical face tangle error at the distance Lf which is an ideal focusposition. However, when the photosensitive member is deviated from theposition of the distance Lf with respect to the mirror face of therotary polygon mirror, the positional deviation cannot be eliminated bythe lens 1001. Here, the distance from the mirror face of the rotarypolygon mirror to the photosensitive member is represented by a distance“x”.

For example, as illustrated in FIG. 17A, when the photosensitive memberis deviated by +a from the distance Lf, the distance to thephotosensitive member is X=Lf+α. In this case, the optical path A of thelaser beam reflected from the mirror face 1002 b of the rotary polygonmirror which has an optical face tangle error, has a positionaldeviation of +Δd in a sub-scanning direction (“y” direction of FIG. 17A)at the distance X=Lf+α. Further, for example, when the photosensitivemember is deviated by −α from the distance Lf, the distance to thephotosensitive member is X=Lf−α. In this case, the optical path A of thelaser beam reflected from the mirror face 1002 b of the rotary polygonmirror, which has an optical face tangle error, has a positionaldeviation of −Δd in the sub-scanning direction at the distance X=Lf−α.

FIG. 17B to FIG. 17D are each a graph for showing the mirror face of therotary polygon mirror in the horizontal axis and an amount of opticalface tangle of the mirror face of the rotary polygon mirror in thevertical axis. Each of those graphs is hereinafter referred to as“optical face tangle error profile”. FIG. 17B is an optical face tangleerror profile when a focus is deviated by a distance “α” in a “+x”direction from the distance Lf which is the ideal focus position. FIG.17C is an optical face tangle error profile of the distance Lf which isthe just focus correction position, in which positional deviation iseliminated by the lens 1001. FIG. 17D is an optical face tangle errorprofile when a focus is deviated by the distance “α” in a “−x” directionfrom the distance Lf which is the just focus correction position. Theamount of optical face tangle is reversed between positive and negativein FIG. 17B and FIG. 17D.

Further, a positional deviation amount Δd in the sub-scanning directionincreases along with an increase in deviation amount of a focus, thatis, “a”. Therefore, the amount of optical face tangle of the mirror faceof the rotary polygon mirror is uniquely determined by the relationshipbetween the angle of the mirror face of the rotary polygon mirror andthe distance “x”. Thus, when the positional deviation (α) occurs in thefocus depth direction (“x” direction), positional deviation (Δd) occursin the sub-scanning direction to change the amount of banding.

<Overall Configuration of Image Forming Apparatus>

FIG. 1A is a schematic cross-sectional view of a digital full-colorprinter (color image forming apparatus) configured to perform imageformation by using toners of a plurality of colors. An image formingapparatus 100 according to an embodiment of the present invention willbe described with reference to FIG. 1A. The image forming apparatus 100includes four image forming portions (image forming units) 101Y, 101M,101C, and 101Bk (broken line portions) respectively configured to formimages of different colors. The image forming portions 101Y, 101M, 101C,and 101Bk form images by using toners of yellow, magenta, cyan, andblack, respectively. Reference symbols Y, M, C, and Bk denote yellow,magenta, cyan, and black, respectively, and suffixes Y, M, C, and Bk areomitted in the description below unless a particular color is described.

The image forming portions 101 each include a photosensitive drum 102,being a photosensitive member. A charging device 103, a light scanningdevice 104, and a developing device 105 are arranged around each of thephotosensitive drums 102. A cleaning device 106 is further arrangedaround each of the photosensitive drums 102. An intermediate transferbelt 107 of an endless belt type is arranged under the photosensitivedrums 102. The intermediate transfer belt 107 is stretched around adrive roller 108 and driven rollers 109 and 110, and rotates in adirection of an arrow B (clockwise direction) illustrated in FIG. 1Awhile forming an image. Further, primary transfer devices 111 arearranged at positions opposed to the photosensitive drums 102 across theintermediate transfer belt 107 (intermediate transfer member). The imageforming apparatus 100 according to the embodiment further includes asecondary transfer device 112 configured to transfer the toner image onthe intermediate transfer belt 107 onto a sheet S being a recordingmedium and a fixing device 113 configured to fix the toner image on thesheet S.

An image forming process from a charging step to a developing step ofthe image forming apparatus 100 will be described. The image formingprocess is the same in each of the image forming portions 101, and hencethe image forming process will be described with reference to an exampleof the image forming portion 101Y. Accordingly, descriptions of theimage forming processes in the image forming portions 101M, 101C, and101Bk are omitted. The photosensitive drum 102Y which is driven torotate in the arrow direction (counterclockwise direction) illustratedin FIG. 1A is charged by the charging device 103Y of the image formingportion 101Y. The charged photosensitive drum 102Y is exposed by a laserbeam emitted from the light scanning device 104Y, which is indicated bythe dashed dotted line. With this operation, an electrostatic latentimage is formed on the rotating photosensitive drum 102Y (on thephotosensitive member). The electrostatic latent image formed on thephotosensitive drum 102Y is developed as a toner image of yellow by thedeveloping device 105Y. The same step is performed also in the imageforming portions 101M, 101C, and 101Bk.

The image forming process from a transfer step will be described. Theprimary transfer devices 111 applied with a transfer voltage transfertoner images of yellow, magenta, cyan, and black formed on thephotosensitive drums 102 of the image forming portions 101 onto theintermediate transfer belt 107. With this, the toner images ofrespective colors are superimposed one on another on the intermediatetransfer belt 107. That is, the toner images of four colors aretransferred onto the intermediate transfer belt 107 (primary transfer).The toner images of four colors transferred onto the intermediatetransfer belt 107 are transferred onto the sheet S conveyed from amanual feed cassette 114 or a sheet feed cassette 115 to a secondarytransfer portion by the secondary transfer device 112 (secondarytransfer). Then, the unfixed toner images on the sheet S are heated andfixed onto the sheet S by the fixing device 113, to thereby form afull-color image on the sheet S. The sheet S having the image formedthereon is delivered to a delivery portion 116.

<Photosensitive Drum and Light Scanning Device>

FIG. 1B is an illustration of configurations of the photosensitive drum102, the light scanning device 104, and a controller for the lightscanning device 104. The light scanning device 104 includes a laserlight source 201, a collimator lens 202, a cylindrical lens 203, and arotary polygon mirror 204. The laser light source 201 includes aplurality of light emitting points. The plurality of light emittingpoints are each configured to emit a laser beam (light beam). Thecollimator lens 202 is configured to collimate the laser beam. Thecylindrical lens 203 condenses the laser beam having passed through thecollimator lens 202 in a sub-scanning direction. In the embodiment, thelaser light source 201 will be described by exemplifying a light sourcein which a plurality of light emitting points are arranged, but issimilarly operated also in the case of using a single light source. Thelaser light source 201 is driven by a laser drive circuit 304. Therotary polygon mirror 204 is formed of a motor portion configured to beoperated to rotate and a reflection mirror mounted on a motor shaft. Aface of the reflection mirror of the rotary polygon mirror 204 ishereinafter referred to as “mirror face”. The rotary polygon mirror 204is driven by a rotary polygon mirror drive portion (hereinafter referredto as “mirror drive portion”) 305. The light scanning device 104includes fθ lenses 205 and 206 configured to receive a laser beam(scanning light) deflected by the rotary polygon mirror 204. Further,the light scanning device 104 includes a memory 302 which is a storageunit configured to store various pieces of information.

Further, the light scanning device 104 includes a beam detector 207(hereinafter referred to as “BD 207”) which is a signal generating unitconfigured to detect the laser beam deflected by the rotary polygonmirror 204 and output a horizontal synchronization signal (hereinafterreferred to as “BD signal”) in accordance with the detection of thelaser beam. The laser beam output from the light scanning device 104scans the photosensitive drum 102. The direction of the laser beam issubstantially parallel to the rotary shaft of the photosensitive drum102. Every time the mirror face of the rotary polygon mirror 204 scansthe photosensitive drum 102, the light scanning device 104 causes alaser beam emitted from the laser light source to move (scan) in themain scanning direction, to thereby form scanning lines corresponding tothe number of laser elements (light emitting points) simultaneously. Inthe embodiment, a configuration is described in which the rotary polygonmirror 204 has five mirror faces, and the laser light source 201includes eight laser elements, as an example. Specifically, in theembodiment, an image of eight lines is formed with one scanning. Therotary polygon mirror 204 scans the photosensitive drum 102 five timesper one revolution or the rotary polygon mirror 204, to thereby form animage of forty lines in total.

The photosensitive drum 102 includes a rotary encoder 301 on the rotaryshaft, and the rotation speed of the photosensitive drum 102 is detectedwith the use of the rotary encoder 301. The rotary encoder 301 isconfigured to generate 1,000 pulses per one revolution of thephotosensitive drum 102. The rotary encoder 301 is configured to measurea time interval between the generated pulses using a built-in timer. Therotary encoder 301 is configured to output information (rotation speeddata) on the rotation speed of the photosensitive drum 102 to a CPU 303based on measurement results. A known speed detection technology otherthan the above-mentioned rotary encoder 301 may be used as long as therotation speed of the photosensitive drum 102 can be detected. As amethod other than the use of the rotary encoder 301, there is given, forexample, a configuration to detect the surface speed of thephotosensitive drum 102 with a laser Doppler.

<Block Diagram of CPU>

Next, the CPU 303 serving as a controller configured to control thelight scanning device 104, and a clock signal generating portion 308 aredescribed with reference to FIG. 2. The CPU 303 and the clock signalgenerating portion 308 are mounted on the image forming apparatus 100.FIG. 2 is a block diagram for illustrating the functions of the CPU 303configured to execute correction processing of correcting distortion anduneven image density of an image described later as a correction unit, atransformation unit, and a filtering unit. The CPU 303 includes afiltering portion 501, an error diffusion processing portion 502, and aPWM signal generating portion 503. The filtering portion 501 isconfigured to perform filtering by subjecting input image data to aconvolution operation. The error diffusion processing portion 502 isconfigured to subject the image data after the filtering to errordiffusion processing. The PWM signal generating portion 503 isconfigured to subject the image data (density data) after the errordiffusion processing to PWM transformation and output a PWM signal tothe laser drive circuit 304 of the light scanning device 104. The clocksignal generating portion 308 is configured to output a clock signalCLK(1) and a clock signal CLK(2) to the CPU 303. The clock signal CLK(1)is a clock signal illustrated in FIG. 5. The clock signal CLK(1) is asignal generated by multiplying the clock signal CLK(2). Thus, the clocksignal CLK(1) and the clock signal CLK(2) have a synchronizationrelationship. In the embodiment, the clock signal generating portion 308outputs the clock signal CLK(1) generated by multiplying the clocksignal CLK(2) by 16 to the CPU 303. The clock signal CLK(2) is a signalhaving a period corresponding to one pixel. The clock signal CLK(1) is asignal having a period corresponding to divided pixels obtained bydividing one pixel by 16.

Further, the CPU 303 includes a filter coefficient setting portion 504,a filter function output portion 505, and a correction value settingportion 506. The filter function output portion 505 is configured tooutput data on a function to be used for a convolution operation (forexample, data in a table) to the filter coefficient setting portion 504.As a function to be used for the convolution operation, there is given,for example, linear interpolation and bicubic interpolation. Thecorrection value setting portion 506 is configured to calculate apositional deviation amount in the rotation direction of thephotosensitive drum 102 of a scanning line formed with a laser beamdeflected by a mirror face identified by a face identifying portion 507,based on information on a positional deviation amount of a lightemitting point of the laser light source 201 and an amount of opticalface tangle of the mirror face of the rotary polygon mirror 204, whichare read from the memory 302 of the optical scanning device 104, and aface synchronization signal input from the face identifying portion 507.In a first embodiment described later, the correction value settingportion 506 is configured to correct an amount of optical face tangle ofthe mirror face of the rotary polygon mirror 204 with an amplitude gainGb corresponding to an image selected from a test chart described later.Further, in a second embodiment described later, the correction valuesetting portion 506 is configured to calculate the amplitude gain Gbbased on focus distance information Δx stored in the memory 302 andcorrect an amount of optical face tangle of the mirror face of therotary polygon mirror 204 with the calculated amplitude gain Gb. Thecorrection value setting portion 506 is configured to calculate acorrection value based on the positional deviation amount of thescanning line and output the calculated correction value to the filtercoefficient setting portion 504. The filter coefficient setting portion504 is configured to calculate a filter coefficient to be used for thefiltering in the filtering portion 501 based on information on theconvolution function input from the filter function output portion 505and the correction value of the scanning line input from the correctionvalue setting portion 506. The filter coefficient setting portion 504 isconfigured to set the calculated filter coefficient in the filteringportion 501. The correction value input to the filter coefficientsetting portion 504 from the correction value setting portion 506 is acorrection value set individually for each of the plurality of mirrorfaces.

Further, the CPU 303 includes the face identifying portion 507. The faceidentifying portion 507 is configured to identify a mirror face of therotary polygon mirror 204 based on an HP signal input from a homeposition sensor (hereinafter referred to as “HP sensor”) 307 of thelight scanning device 104 and the BD signal input from the BD 207. Theface identifying portion 507 is configured to output information of theidentified mirror face to the correction value setting portion 506 as aface synchronization signal.

As illustrated in FIG. 1B, the CPU 303 is configured to receive imagedata from an image controller (not shown) configured to generate imagedata. The image data is tone data indicating a density value. The tonedata is data of a plurality of bits indicating a density value for eachpixel. For example, in the case of image data of 4 bits, a density valuefor one pixel is expressed by 16 tones, and in the case of image data of8 bits, a density value for one pixel is expressed by 256 tones. In theembodiment, the image data input to the CPU 303 from the imagecontroller is 4 bits per pixel. The filtering portion 501 is configuredto subject the image data to filtering for each pixel in synchronizationwith the clock signal CLK(2). Further, in the first embodiment describedlater, the amplitude gain Gb described later is also input to the CPU303. The CPU 303 is connected to the rotary encoder 301, the BD 207, thememory 302, the laser drive circuit 304, and a mirror drive portion 305.The CPU 303 is configured to detect a write position of a scanning linebased on the BD signal input from the BD 207 and count a time intervalof the BD signal, to thereby detect the rotation speed of the rotarypolygon mirror 204. Further, the CPU 303 is configured to output anacceleration or deceleration signal for designating acceleration ordeceleration to the mirror drive portion 305 so that the rotary polygonmirror 204 reaches a predetermined speed. The mirror drive portion 305is configured to supply a driving current to the motor portion of therotary polygon mirror 204 in accordance with the acceleration ordeceleration signal input from the CPU 303, to thereby drive a motor306.

As illustrated in FIG. 2, the HP sensor 307 is mounted on the rotarypolygon mirror 204 and is configured to output the HP signal to the CPU303 at timing at which the rotary polygon mirror 204 reaches apredetermined angle during a rotation operation. For example, the HPsignal is generated once during every rotation of the rotary polygonmirror 204. The face identifying portion 507 resets an internal counterin response to the generation of the HP signal. Then, the faceidentifying portion 507 increments a count value of the internal counterby “1” every time the BD signal is input. That is, each count value ofthe internal counter is information indicating a corresponding one ofthe plurality of mirror faces of the rotary polygon mirror 204. The CPU303 can identify which of the plurality of mirror faces the input imagedata corresponds to with the use of the count value. That is, the CPU303 can switch a filter coefficient for correcting the input image datawith the use of the count value.

The memory 302 is configured to store, for each mirror face, positioninformation (first scanning position information) indicating positionaldeviation amounts from ideal scanning positions in the sub-scanningdirection of a plurality of laser beams reflected by the mirror faces ofthe rotary polygon mirror 204. Further, the memory 302 is configured tostore position information (second scanning position information)indicating a positional deviation amount from the ideal scanningposition in the sub-scanning direction of the laser beam emitted fromeach light emitting point. The CPU 303 is configured to read from thememory 302 positional deviation information in the sub-scanningdirection caused by an optical face tangle error for each mirror face ofthe rotary polygon mirror 204 and positional deviation information of amultibeam laser of 1,200 dpi with respect to the ideal position in thesub-scanning direction. The CPU 303 is configured to calculate positioninformation of each scanning line based on the positional deviationinformation read from the memory 302.

The correction value setting portion 506 is configured to calculate acorrection value based on the position information of each scanning lineinput from the memory 302 and output the calculated correction value tothe filter coefficient setting portion 504. The filter coefficientsetting portion 504 is configured to calculate a filter coefficient withthe use of the correction value input from the correction value settingportion 506 and a filter function input from the filter function outputportion 505. The filtering portion 501 is configured to receive imagedata from the image controller (not shown) configured to generate imagedata. The filtering portion 501 is configured to subject the image datato the filtering based on the filter coefficient input from the filtercoefficient setting portion 504, to thereby calculate image data takinginformation for correcting the position of each scanning line intoaccount. The PWM signal generating portion 503 of the CPU 303 isconfigured to convert the image data taking the information forcorrecting the position of each scanning line into account into drivedata. A ROM 309 is configured to store a conversion table for convertingimage data of 4 bits into drive data of 16 bits as shown in FIG. 18. Thevertical axis of the conversion table shown in FIG. 18 represents imagedata indicating density values of 4 bits, which corresponds to onepixel. The horizontal axis of the conversion table shown in FIG. 18represents drive data of 16 bits associated with the density values of 4bits individually. For example, in the case where image data input tothe PWM signal generating portion 503 is a bit pattern of “0110”, thePWM signal generating portion 503 converts the image data “0110” intodrive data which is a bit pattern of “0000000001111111” with the use ofthe conversion table. The PWM signal generating portion 503 outputs theconverted drive data in the order of “0000000001111111” serially on abit basis in accordance with the clock signal CLK(1) described later.When the PWM signal generating portion 503 outputs the drive data, a PWMsignal is generated. When the PWM signal generating portion 503 outputs“1”, a light emitting point emits a laser beam. When the PWM signalgenerating portion 503 outputs “0”, a light emitting point does notoutput a laser beam.

<Scanning Position Information>

Next, scanning position information stored in the memory 302 will bedescribed with reference to FIG. 3 and Table 1. FIG. 3 is anillustration of a state of positional deviation of each scanning linefrom an ideal position. Scanning lines scanned by each laser beam of thelaser light source having eight light emitting points are denoted byLD1, LD2, LD3, LD4, LD5, LD6, LD7, and LD8. An ideal interval(predetermined interval) between the respective scanning lines isdetermined based on a resolution. For example, in the case of an imageforming apparatus having a resolution of 1,200 dpi, an ideal intervalbetween the respective scanning lines is 21.16 μm. When the scanningline LD1 is defined as a reference position, ideal distances D2 to D8 ofthe scanning lines LD2 to LD8 from the scanning line LD1 are calculatedby Expression (1).Dn=(n−1)×21.16 μm(n=2 to 8)  Expression (1)

For example, the ideal distance D4 from the scanning line LD1 to thescanning line LD4 is 63.48 μm (=(4−1)×21.16 μm).

In this case, an interval between the scanning lines on thephotosensitive drum 102 has an error due to an error of arrangementintervals of the plurality of light emitting points and characteristicsof a lens. The positional deviation amounts of the scanning lines LD2 toLD8 with respect to ideal positions determined based on the idealdistances D2 to D8 are denoted by X1 to X7. Regarding a face A of therotary polygon mirror 204, for example, the positional deviation amountX1 of the scanning line LD2 is defined as a difference between the idealposition of the scanning line LD2 (hereinafter referred to as “LINE 2”,which similarly applies to the other scanning lines) and the actualscanning line. Further, for example, the positional deviation amount X3of the scanning line LD4 is defined as a difference between the LINE 4and the actual scanning line.

Due to a variation in manufacturing of each mirror face of the rotarypolygon mirror 204, the mirror faces of the rotary polygon mirror 204are not completely parallel to the rotary shaft, and the rotary polygonmirror 204 has an angle variation for each mirror face. Further, inscanning of a laser beam on each mirror face, a deviation amount variesdepending on the position in the main scanning direction. In theembodiment, an image area in the main scanning direction is divided intoa predetermined number of blocks, for example, five blocks and an amountof optical face tangle corresponding to each of the five blocks isstored in the memory 302 for each mirror face. When position informationis stored in the memory 302 for each block as described above, acapacity can be reduced as compared to the case where positioninformation is held for each pixel.

When the number of mirror faces of the rotary polygon mirror 204 isfive, and the number of blocks in the main scanning direction is five,amounts of optical face tangle with respect to ideal positions in therespective mirror faces of the rotary polygon mirror 204 are representedby Y1A to Y5E. In this case, A to E represent five faces of the rotarypolygon mirror 204, and 1 to 5 represent five blocks in the mainscanning direction. For example, amounts of optical face tangle from theideal positions of the first to fifth blocks in the scanning line(LINE 1) LD1 of the face A of the rotary polygon mirror 204 arerepresented by Y1A, Y2A, Y3A, Y4A, and Y5A. Similarly, deviation amountsfrom the ideal positions of the first to fifth blocks in the scanningline (LINE 9) LD1 of a face B of the rotary polygon mirror 204 arerepresented by Y1B, Y2B, Y3B, Y4B, and Y5B.

In the embodiment, a positional deviation amount is calculated based onthe amounts of optical face tangle Y1A to Y5E described above and anamount obtained by integrating the amplitude gain Gb. The embodiment hasa configuration in which the amplitude gain Gb can be input to theamounts of optical face tangle (Y1A to Y5E) measured in the singleoptical scanning device 104 from the image forming apparatus 100 side,and a correction amount for correcting banding is adjusted. Further, theamplitude gain Gb is a value determined based on a positional deviationamount (which is the above-mentioned ±Δd and is also an amount ofoptical face tangle) from the ideal optical path B of the optical path Aof the light scanning device 104 illustrated in FIG. 17A. A method ofdetermining the amplitude gain Gb will be described in the embodimentslater.

A total positional deviation amount of an amount of optical face tangleof an m-th mirror face of the rotary polygon mirror 204 and a positionaldeviation amount of the b-th block in the main scanning direction of ann-th laser beam of the laser light source (hereinafter simply referredto as “positional deviation amount”) is represented by Znbm. Then, thepositional deviation amount Znbm is represented by Expression (2) withthe use of the positional deviation amounts X1 to X7 in the sub-scanningdirection of the respective scanning lines, the amounts of optical facetangle YA to YE of the respective mirror faces, and the amplitude gainGb.Znbm=YbmxGb+X(n−1)  Expression (2)

-   -   (n=1 to 8, b=1 to 5, m=A to E)    -   (where X(0)=0)

For example, a positional deviation amount Z43A of the third block inthe scanning line LD4 of the face A of the rotary polygon mirror 204 isdetermined to be Z43A=Y3A×G3+X3 by Expression (2). Further, a positionaldeviation amount Z15B of the fifth block in the scanning line LD1 of theface B of the rotary polygon mirror 204 is determined to be Z15B=Y5B×G5by Expression (2). The first term “YbmxGb” of the right side ofExpression (2) is an amount of optical face tangle obtained bycorrecting the amount of optical face tangle of the mirror face of therotary polygon mirror 204 with the use of the amplitude gain Gb.

When the positional deviation amount Znbm is calculated by Expression(2), it is only necessary that the number of pieces of data to be usedfor calculating the positional deviation amount Znbm correspond to thenumber of the mirror faces of the rotary polygon mirror 204, the numberof light emitting points of the laser light source, and the number ofblocks in the main scanning direction. An address map of positionaldeviation data stored in the memory 302 is shown in Table 1.

TABLE 1 Address Data 1 LD2 position information X1 2 LD3 positioninformation X2 3 LD4 position information X3 4 LD5 position informationX4 5 LD6 position information X5 6 LD7 position information X6 7 LD8position information X7 8 Face A position information Y1A 9 Face Aposition information Y2A 10 Face A position information Y3A 11 Face Aposition information Y4A 12 Face A position information Y5A 13 Face Bposition information Y1B 14 Face B position information Y2B 15 Face Bposition information Y3B 16 Face B position information Y4B 17 Face Bposition information Y5B 18 Face C position information Y1C 19 Face Cposition information Y2C 20 Face C position information Y3C 21 Face Cposition information Y4C 22 Face C position information Y5C 23 Face Dposition information Y1D 24 Face D position information Y2D 25 Face Dposition information Y3D 26 Face D position information Y4D 27 Face Dposition information Y5D 28 Face E position information Y1E 29 Face Eposition information Y2E 30 Face E position information Y3E 31 Face Eposition information Y4E 32 Face E position information Y5E

As shown in Table 1, in the addresses 1 to 7 of the memory 302,information on the respective positional deviation amounts (described asposition information) X1 to X7 of the scanning line LD2 to the scanningline LD8 is stored. Further, in the addresses 8 to 12 of the memory 302,information on the respective positional deviation amounts Y1A to Y5A ofthe blocks 1 to 5 of the mirror face A of the rotary polygon mirror 204is stored. Further, in the addresses 13 to 17 of the memory 302,information on the respective positional deviation amounts Y1B to Y5B ofthe blocks 1 to 5 of the mirror face B of the rotary polygon mirror 204is stored. Further, in the addresses 18 to 22 of the memory 302,information on the respective positional deviation amounts Y1C to Y5C ofthe blocks 1 to 5 of the mirror face C of the rotary polygon mirror 204is stored. Further, in the addresses 23 to 27 of the memory 302,information on the respective positional amounts Y1D to Y5D of theblocks 1 to 5 of the mirror face D of the rotary polygon mirror 204 isstored. Further, in the addresses 28 to 32 of the memory 302,information on the positional deviation amounts Y1E to Y5E of the blocks1 to 5 of the mirror face E of the rotary polygon mirror 204 is stored.

(Memory Storage Operation)

As information on a positional deviation amount to be stored in thememory 302, for example, data measured in an adjustment step of thelight scanning device 104 in a factory or the like is stored. Further,the image forming apparatus 100 may include a position detection unitconfigured to detect the position of a scanning line formed with a laserbeam emitted from the laser light source 201 so that the informationstored in the memory 302 may be updated in real time. As the positiondetection unit configured to detect a position of scanning light in thesub-scanning direction, a known technology may be used. For example, aposition may be detected by a CMOS sensor or a position sensitivedetector (PSD) arranged in the light scanning device 104 or arranged ona scanning path of a laser beam near the photosensitive drum 102.Further, a triangular slit may be formed in a surface of a photo diode(PD) arranged in the light scanning device 104 or arranged near thephotosensitive drum 102, to thereby detect a position from an outputpulse width of the PD.

FIG. 4 is a block diagram for illustrating a step of storing informationin the memory 302 of the light scanning device 104 in a factory or thelike as an example. The same configurations as those of FIG. 2 aredenoted by the same reference symbols as those therein, and thedescription thereof is omitted. In the adjustment step for the lightscanning device 104, a measuring instrument 400 is arranged at aposition corresponding to the scanning position on the photosensitivedrum 102 when the light scanning device 104 is mounted on the imageforming apparatus 100. The measuring instrument 400 includes a measuringportion 410 and a calculation portion 402, and the calculation portion402 is configured to receive a face synchronization signal from the faceidentifying portion 507 of the CPU 303 of FIG. 2. In the CPU 303 of FIG.4, only the face identifying portion 507 is illustrated. First, a laserbeam is radiated on the measuring portion 410 from the light scanningdevice 104. The measuring portion 410 includes a triangular slit 411 anda PD 412. A laser beam emitted from the light scanning device 104indicated by the arrow with the alternate long and short dash line inFIG. 4 scans the triangular slit 411. The measuring portion 410 measuresthe position in the sub-scanning direction of a scanning line based oninformation on the laser beam input to the PD 412 through the triangularslit 411. The measuring portion 410 outputs information on the measuredposition in the sub-scanning direction, which depends on themain-scanning direction, of the scanning line in each mirror face(hereinafter referred to as “data for each face”) of the rotary polygonmirror 204 to the calculation portion 402.

Meanwhile, the face identifying portion 507 is configured to receive theHP signal from the HP sensor 307 of the light scanning device 104 andreceive the BD signal from the BD 207. With this, the face identifyingportion 507 is configured to identify a mirror face of the rotarypolygon mirror 204 and output information on the identified mirror faceto the calculation portion 402 as a face synchronization signal. Thecalculation portion 402 is configured to write the information on theposition in the sub-scanning direction, which depends on themain-scanning direction, of the scanning line measured by the measuringportion 410 into an address on the memory 302 of the light scanningdevice 104 in accordance with the information on the mirror face of therotary polygon mirror 204 input from the face identifying portion 507.Thus, the information on the positional deviation amounts of thescanning lines caused by a variation in intervals between the eightlight emitting points of the laser light source 201 (X1 to X7) is storedin the memory 302. Further, the information on the positional deviationamounts of the scanning lines caused by an optical face tangle error ofthe mirror face of the rotary polygon mirror 204 (Y1 to Y5) for eachblock is also stored in the memory 302.

<Method of Calculating Positional Deviation Amount>

FIG. 5 is a diagram for illustrating control timing in one scanningperiod of the n-th laser beam in the sub-scanning direction of theembodiment. (1) represents a CLK signal corresponding to a pixel periodper pixel ( 1/16 pixel) obtained by dividing one pixel by 16. (2)represents input timing of a BD signal from the BD 207 with respect tothe CPU 303. (3) and (5) represent input timing of image data DATAN(N=1, 2, . . . ) before filtering with respect to the CPU 303. (4)represents timing at which a positional deviation amount CnN (N=1, 2, .. . ) corresponding to each pixel is calculated. (6) represents timingat which image data DATAN′ (N=1, 2, . . . ) subjected to the filteringis output to the laser drive circuit 304. N at the end of DATAN andDATAN′ represents a number of a pixel in one scanning line in the mainscanning direction.

When the BD signal output from the BD 207 is defined as a reference, atime is represented by T1, which is from the input of the BD signal tothe CPU 303 to the start of the processing of image data input to theCPU 303 during a period from the input of the BD signal to the CPU 303to the input of a subsequent BD signal. Further, a time is representedby T2, which is from the input of the BD signal to the CPU 303 to thecompletion of the output of the image data input to the CPU 303 during aperiod from the input of the BD signal to the CPU 303 to the input of asubsequent BD signal. The CPU 303 stands by until the predetermined timeT1 elapses after the input of the BD signal, and starts filtering of theinput image data in synchronization with the clock signal CLK (2) togenerate drive data successively from the processed image data. Then,the CPU 303 outputs the drive data by one bit to output a PWM signal tothe laser drive circuit 304. Then, the CPU 303 ends the processing ofthe image data in one scanning line after the predetermined time T2elapses after the input of the BD signal. The CPU 303 calculates apositional deviation amount of a scanning line in the scanning periodduring a period in which the predetermined time T1 elapses from thedetection of the BD signal, that is, a period in which a laser beamscans a non-image area. Then, the CPU 303 causes the filter coefficientsetting portion 504 to set a filter coefficient based on the calculatedpositional deviation amount. The CPU 303 causes the filtering portion501 to correct the image data with the use of the filter coefficient setby the filter coefficient setting portion 504 for each scanning untilthe predetermined time T2 elapses after the predetermined time T1elapses. That is, the CPU 303 calculates a positional deviation amountof a scanning line in the image area and sends the image data after thefiltering by the filtering portion 501 to the laser drive circuit 304,to thereby form an image. In this case, a positional deviation amountwith respect to a pixel of interest is calculated during a time of oneperiod of the CLK signal of (1). Further, the filtering with respect tothe pixel of interest is performed by the filtering portion 501 during atime of one period of the CLK signal of (1). Then, after one clock fromthe input of the image data before filtering, the image data afterfiltering is output to the laser drive circuit 304 (broken frame part ofFIG. 5). A time interval of the BD signal output from the BD 207 isrepresented by ΔT, which corresponds to a time per scanning.

In the embodiment, the positional deviation amount (CnN) of each pixelrepresented by (4) of FIG. 5 is calculated with the use of thepositional deviation amounts of the five blocks (b=1 to 5) divided inthe main scanning direction. The positional deviation amount of eachpixel may be obtained by subjecting the positional deviation amounts ofthe respective blocks to linear interpolation and sorting the resultantpositional deviation amounts to positional deviation amounts of therespective pixels. One positional deviation amount may correspond to onepixel in the main scanning direction, or one positional deviation amountmay correspond to a plurality of pixels. Through the above-mentionedoperation, between the time T1 and the time T2, the CPU 303 calculates apositional deviation amount, performs filtering, and sends the imagedata to the laser drive circuit 304, to thereby form an image for onescanning.

(Calculation of Positional Deviation Amount of N-th Pixel)

FIG. 6 is a flowchart for illustrating processing of forming an imagewhile calculating a positional deviation amount of an N-th pixel in themain scanning direction, which is performed by the CPU 303. The CPU 303calculates a positional deviation amount for each scanning line duringimage formation, to thereby form an image. In Step (hereinafterabbreviated as “S”) 7001, that is, in S7001, the CPU 303 sets a positionn in the sub-scanning direction to 1. The CPU 303 determines in S7002whether or not the BD signal has been input from the BD 207. When theCPU 303 determines in S7002 that the BD signal has been input, the CPU303 stops a timer (not shown) configured to measure a time intervalcorresponding to a period of the BD signal and reads and stores a timervalue in an internal register. Then, the CPU 303 resets and starts thetimer (not shown) in order to measure a time interval until a subsequentBD signal is received and proceeds to the processing of S7003. When theCPU 303 includes two or more timers (not shown), the CPU 303 mayalternately use the different timers every time the BD signal isreceived, to thereby measure a time interval. Although the measured timeinterval of the BD signal is stored in the internal register of the CPU303, the CPU 303 may store the time interval in, for example, a RAM (notshown). When the CPU 303 determines in S7002 that the BD signal has notbeen input, the CPU 303 returns to the processing of S7002 in order towait for input of the BD signal.

In S7003, the CPU 303 refers to the timer, to thereby determine whetheror not the time T1 has elapsed from the detection of the BD signal. Whenthe CPU 303 determines in S7003 that the time T1 has elapsed, the CPU303 determines that the laser beam has entered the image area in themain scanning direction and proceeds to the processing of S7004. Whenthe CPU 303 determines in S7003 that the time T1 has not elapsed, theCPU 303 determines that the laser beam is still in the non-image area inthe main scanning direction and returns to the processing of S7003. InS7004, the CPU 303 sets a variable N to 1. In this case, the variable Nis a variable corresponding to a pixel number from an image writeleading pixel in the main scanning direction. In S7005, the CPU 303calculates a positional deviation amount (CnN) of the N-th pixel in themain scanning direction ((4) of FIG. 5) and subjects the image data tofiltering based on the positional deviation amount ((5) and (6) of FIG.5). The CPU 303 determines in S7006 whether or not N is 14,000. When theCPU 303 determines that N is 14,000, the CPU 303 proceeds to theprocessing of S7008. When the CPU 303 determines in S7006 that N is not14,000, the CPU 303 proceeds to the processing of S7007. In S7007, theCPU 303 adds 1 to N (N=N+1), and returns to the processing of S7005 inorder to subject a subsequent pixel in the main scanning direction tocalculation. In this case, for example, when an image is formed with aresolution of 1,200 dpi on a recording sheet of an A4 size (length inthe main scanning direction is 297 mm), the number of pixels is about14,000. Therefore, when a positional deviation amount of each pixel iscalculated by changing the pixel number N within a range of from 1 to14,000 in the main scanning direction, a positional deviation amount ofone scanning is calculated. When the resolution is changed, thethreshold value of S7006 is also changed to a value in accordance withthe resolution.

In S7008, the CPU 303 adds 1 to the position n in the sub-scanningdirection (n=n+1) and proceeds to the processing of S7009. The CPU 303determines in S7009 whether or not the processing of one page has beencompleted based on the position n in the sub-scanning direction. Whenthe CPU 303 determines that the processing has been completed, the CPU303 ends the processing. When the CPU 303 determines that the processinghas not been completed, the CPU 303 returns to the processing of S7002.

(Calculation of Positional Deviation Amount)

A calculation expression of the positional deviation amount CnNcalculated by the CPU 303 in S7005 will be described in detail. Thepositional deviation amount CnN of an n-th scanning line with respect tothe pixel number N in the main scanning direction is determined asfollows. That is, the positional deviation amount CnN is determined byadding a positional deviation amount A caused by a change in rotationspeed of the photosensitive drum 102 and the rotary polygon mirror 204to a positional deviation amount B that depends on the main scanningdirection for each scanning line, to thereby calculate a totalpositional deviation amount. When the rotation speed of thephotosensitive drum 102 is represented by Vd, the rotation speed of therotary polygon mirror 204 is represented by Vp, and one scanning time isrepresented by ΔT (see FIG. 5), the positional deviation amount A causedby a speed difference between the rotation speed Vd of thephotosensitive drum 102 and the rotation speed Vp of the rotary polygonmirror 204 is calculated by the following Expression (3).A=(Vd−Vp)×ΔT  Expression (3)

In this case, ΔT represents a time corresponding to an interval ofoutput timing of the BD signal, and the positional deviation amount Arepresents a positional deviation amount of a scanning line that movesduring one scanning period due to a difference between the rotationspeed Vd of the photosensitive drum 102 and the rotation speed Vp of therotary polygon mirror 204. In this case, as described above, therotation speed Vp of the rotary polygon mirror 204 is determined basedon a printing speed Vpr. The printing speed Vpr is determined byExpressions (4) and (5) based on the relationship between the onescanning time ΔT and the multi-beam number (eight beams in theembodiment).Vp=Number of beams×21.16/ΔT  Expression (4)ΔT=1/(Number of mirror faces of rotary polygon mirror 204×Revolutionnumber per second of rotary polygon mirror 204)  Expression (5)

Meanwhile, as the positional deviation amount B, a value calculated byExpression (2) is used.B=Znbm  Expression (6)

The CPU 303 adds the positional deviation amount A calculated byExpression (3) to the positional deviation amount B calculated byExpression (6), to thereby calculate a total positional deviation amount(total value=A+B). The CPU 303 holds the total positional deviationamount calculated in S7005 in the internal register of the CPU 303. Inthis case, the total positional deviation amount (=A+B) held in theinternal register is read and used for calculation during filteringdescribed later.

In the embodiment, the CPU 303 subjects image data on a plurality ofscanning lines to calculation with the use of a filter set based on thepositional deviation amount calculated for each scanning line.Therefore, in the above-mentioned positional deviation amountcalculation operation, the CPU 303 determines positional deviationamounts of the plurality of scanning lines to be used for filtering,during a period from the output of the BD signal from the BD 207 to theelapse of the time T1. When the range of filtering is, for example, L=3,the CPU 303 refers to the image data on three pixels above and below aline of interest and calculates a positional deviation amount of eachscanning line within the range of the three pixels above and below theline of interest, to thereby perform filtering.

In this case, a positional deviation amount of a scanning linecorresponding to the line of interest is calculated during a periodimmediately before image formation. Further, calculation results of apositional deviation amount calculated for a scanning line formedpreviously is used for a scanning line formed before the line ofinterest. Regarding a scanning line to be formed at timing after theline of interest, the positional deviation amount B is determined basedon the information on the mirror face of the rotary polygon mirror 204corresponding to a scanning line to be formed later and the positioninformation on a plurality of light emitting points. Further, therotation speed Vp of the rotary polygon mirror 204 and the rotationspeed Vd of the photosensitive drum 102 are determined as follows. Thatis, the rotation speeds Vp and Vd in a scanning line to be scanned nextare respectively predicted to be determined based on a value detected attiming of previous scanning by the laser beam and a value detected attiming of scanning of the line of interest (current scanning line).

(Correction of Position of Pixel of Input Image in Sub-ScanningDirection)

In the embodiment, the CPU 303 is configured to correct image data basedon the positional deviation amounts in the sub-scanning direction of thescanning lines formed by laser beams and output the corrected image datato the laser drive circuit 304. Now, a flowchart of FIG. 7 will bedescribed below. FIG. 7 is a flowchart for illustrating correctionprocessing for correcting uneven image density and banding caused by thepositional deviation in the sub-scanning direction. In 53602, the CPU303 reads the positional deviation amount in the sub-scanning directionand the amount of optical face tangle stored in the memory 302.Specifically, the CPU 303 reads the position information X1 to X7 of thescanning lines LD2 to LD8 and the position information Y1A to Y5Ecorresponding to the respective blocks of the faces A to E of the rotarypolygon mirror 204 shown in Table 1 from the memory 302. In the case ofthe second embodiment described later, the CPU 303 also reads focusdistance information Δx1 to Δx5 from the memory 302. In the embodiment,a pixel position of input image data in the sub-scanning direction iscorrected based on the positional deviation amount in the sub-scanningdirection, followed by filtering, to thereby output image data, that is,density.

(State of Positional Deviation of Scanning Line)

The state of positional deviation of a scanning line can be roughlyclassified into four cases. First, regarding the state of positionaldeviation, there is a case (a) in which the position of a scanning line(hereinafter referred to as “scanning position”) on the photosensitivedrum 102 is shifted in an advance direction with respect to an idealscanning position, and a case (b) in which the scanning position on thephotosensitive drum 102 is shifted in a return direction with respect tothe ideal scanning position. Further, regarding the state of positionaldeviation, there is a case (c) in which the intervals between thescanning positions on the photosensitive drum 102 are dense with respectto the intervals between the ideal scanning positions, and a case (d) inwhich the intervals between the scanning positions on the photosensitivedrum 102 are sparse with respect to the intervals between the idealscanning positions. Specific examples of the state of positionaldeviation in the sub-scanning direction are illustrated in FIG. 8A, FIG.8B, FIG. 8C, and FIG. 8D. In FIG. 8A to FIG. 8D, the broken linesrepresent scanning positions, and in FIG. 8A to FIG. 8D, (1) to (5)represent the order of scanning. In the embodiment, eight beams are usedfor scanning simultaneously, but description is given on the assumptionthat the order is allocated to each beam arranged successively in thesub-scanning direction. Each column on the left side of FIG. 8A to FIG.8D represents ideal scanning positions, and each column on the rightside represents scanning positions on the photosensitive drum 102. S1 toS5 represent positional deviation amounts from the ideal scanningpositions with respect to scanning numbers (1) to (5). The unit of apositional deviation amount is represented based on the case where theideal beam interval (21.16 μm at 1,200 dpi) is defined as 1, and theadvance direction of a laser beam in the sub-scanning direction(hereinafter simply referred to as “advance direction”) is set to apositive value. Further, the return direction of the laser beam in thesub-scanning direction (hereinafter simply referred to as “returndirection”) is set to a negative value. Further, in order to describethe state of an image, each pixel arranged in the sub-scanning directionis represented by a circle on the scanning line. The shading of thecircle represents density.

FIG. 8A is an illustration of an example in which the scanning positionson the photosensitive drum 102 are shifted by 0.2 uniformly in theadvance direction from the ideal scanning positions. The positionaldeviation amount as illustrated in FIG. 8A is hereinafter referred to asa shift amount of +0.2. FIG. 8B is an illustration of an example inwhich the scanning positions on the photosensitive drum 102 are shiftedby 0.2 uniformly in the return direction from the ideal scanningpositions. The positional deviation amount as illustrated in FIG. 8B ishereinafter referred to as a shift amount of −0.2. In FIG. 8A and FIG.8B, the scanning positions are shifted uniformly, and hence the intervalbetween the scanning positions on the photosensitive drum 102 is 1 inboth the cases.

In FIG. 8C, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in theadvance direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the return direction increases.For example, S3 is +0 in the scanning number (3), but S2 is +0.2 in thescanning number (2), S1 is +0.4 in the scanning number (1), S4 is −0.2in the scanning number (4), and S5 is −0.4 in the scanning number (5).In FIG. 8C, the interval between the scanning positions is 0.8, which issmaller than 1. The state of positional deviation as illustrated in FIG.8C is hereinafter referred to as being dense at an interval of a (1-0.2)line.

In FIG. 8D, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in thereturn direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the advance direction increases.For example, S3 is +0 in the scanning number (3), but S2 is −0.2 in thescanning number (2), S1 is −0.4 in the scanning number (1), S4 is +0.2in the scanning number (4), and S5 is +0.4 in the scanning number (5).In FIG. 8D, the interval between the scanning positions is 1.2, which islarger than 1. The state of positional deviation as illustrated in FIG.8D is hereinafter referred to as being sparse at an interval of a(1+0.2) line.

In the dense state as illustrated in FIG. 8C, positional deviationoccurs, and in addition, the intervals between scanning positions aredense to cause pixels to be arranged densely on the photosensitive drum102, with the result that a pixel value per predetermined areaincreases, to thereby increase density. In contrast, in the sparse stateas illustrated in FIG. 8D, positional deviation occurs, and in addition,the intervals between scanning positions are sparse to cause pixels tobe arranged sparsely on the photosensitive drum 102, with the resultthat a pixel value per predetermined area decreases, to thereby decreasedensity. In an electrophotographic process, a shading difference may befurther emphasized due to a relationship between the depth of a latentimage potential and development characteristics. Further, when the denseor sparse state occurs alternately as illustrated in FIG. 8C and FIG.8D, a periodic shading causes moire, which is liable to be detectedvisually even at the same amount depending on a space frequency.

Referring back to the flowchart of FIG. 7, in S3603, the CPU 303generates attribute information for correction of each pixel of an inputimage with the correction value setting portion 506. In the embodiment,the pixel position in the sub-scanning direction of an input image issubjected to coordinate transformation in advance and interpolated,thereby being capable of correcting positional deviation and correctinglocal shading simultaneously while maintaining density of the inputimage. The attribute information for correction specifically refers to acorrection value CnN described later. In this case, “n” represents ascanning line number (or pixel number) in the sub-scanning direction,and N represents a pixel number in the main scanning direction. Thecorrection value CnN means a correction value of the N-th pixel in themain scanning direction in the n-th scanning line in the sub-scanningdirection. In the following description, the N-th pixel in the mainscanning direction of each scanning line will be described, and thecorrection value CnN is simply referred to as C or Cn in some cases.

(Coordinate Transformation)

A method for coordinate transformation according to the embodiment willbe described with reference to FIG. 9A to FIG. 11B. In each graph ofFIG. 9A to FIG. 11B, the horizontal axis represents a pixel number “n”,and the vertical axis represents a pixel position (which is also ascanning position) “y” (y′ after the coordinate transformation) in thesub-scanning direction, with the unit being a line. Further, FIG. 9A,FIG. 9B, FIG. 11A, and FIG. 11B correspond to FIG. 8A to FIG. 8D,respectively. Each graph on the left side of FIG. 9A, FIG. 9B, FIG. 11A,and FIG. 11B represents the state before the coordinate transformation,and each graph on the right side thereof represents the state after they-axis coordinate transformation. Square dots plotted in each graphrepresent scanning positions on the photosensitive drum 102, andcircular dots therein represent ideal scanning positions.

(Case of Being Shifted in Advance Direction and Return Direction)

The graph on the left side of FIG. 9A is first described. In the graphbefore the coordinate transformation, the ideal scanning positionplotted with the circular dots is a position in which, for example, apixel position “y” in the sub-scanning direction is 2 with respect tothe pixel number 2. Thus, the y-coordinate of the pixel position “y” isequal to that of the pixel number “n”, and the ideal scanning positionsare represented by a straight line (indicated by the alternate long andshort dash line) with a gradient of 1. The straight alternate long andshort dash line is represented by Expression (7).y=n  Expression (7)

As illustrated in FIG. 8A, the scanning positions plotted with thesquare dots are shifted by S(=0.2) line in the advance direction (+direction of y-axis) with respect to the ideal scanning positionsplotted with the circular dots. Therefore, the scanning positionsplotted with the square dots are represented by a straight line(indicated by the solid line) offset with the gradient being 1, which isrepresented by Expression (8).y=n+S  Expression (8)

In the embodiment, the coordinate transformation is performed so thatthe actual scanning positions are transformed into the ideal scanningpositions. Therefore, in the example illustrated in FIG. 9A, it is onlynecessary that the coordinate transformation be performed with the useof Expression (9). In Expression (9), C represents a correction amount.y′=y+C  Expression (9)

Thus, the correction amount C is represented by a shift amount S andExpression (10).C=−S  Expression (10)

Through Expression (9) of the coordinate transformation and Expression(10) for determining the correction amount C, Expressions (7) and (8)are converted as represented by Expressions (11) and (12), respectively.y′=y+C=n+(−S)=n−S  Expression (11)y′=y+C=(n+S)+C=(n+S)+(−S)=n  Expression (12)

In FIG. 9B, when the shift amount S is defined as −0.2, Expression (12)similarly holds from Expression (7), and a similar description to thatof FIG. 9A can be given. As illustrated in FIG. 9A and FIG. 9B, when thescanning lines are not sparse or dense, and are shifted in the advancedirection or the return direction, a straight line has a predeterminedgradient before and after the coordinate transformation.

(Case in which Dense or Sparse State Occurs)

Now, the coordinate transformation will be described, the coordinatetransformation being also applicable to the cases in FIG. 11A and FIG.11B in which the scanning positions are dense or sparse, and the casesof combinations of FIG. 9A, FIG. 9B, FIG. 11A, and FIG. 11B in which ashift and a dense or sparse state occur. FIG. 10A is an illustration ofa relationship between the pixel number and the scanning position. Thehorizontal axis represents the pixel number “n”, and the vertical axis“y” represents a scanning position in the sub-scanning direction. Squaredots are plotted as the scanning positions on the photosensitive drum102. In FIG. 10A, the case is described in which the scanning lines aredense on the photosensitive drum 102 within a range of the pixel numberof n≤2, and the scanning lines are sparse on the photosensitive drum 102within a range of the pixel number of n≥2.

As illustrated in FIG. 10A, when the scanning lines are dense within therange of the pixel number of n≤2, and are sparse within the range of thepixel number of n≥2, the gradient of a straight line within the range ofthe pixel number of n≤2 is different from that of a straight line withinthe range of the pixel number of n≥2, and the straight line has a curvedshape at the pixel number of n=2. In FIG. 10A, a function indicating achange in scanning positions passing through the square dots is definedas ft(n) and is represented by the solid line. The function ft(n)representing the scanning positions is represented by Expression (13).y=ft(n)  Expression (13)

Next, when a function after the coordinate transformation of the y-axisthat represents the scanning positions in the sub-scanning direction isdefined as ft′(n), the function ft′(n) representing the scanningpositions after the coordinate transformation is represented byExpression (14).y′=ft′(n)  Expression (14)

In the embodiment, the coordinate transformation is performed byexpanding or contracting the y-axis or shifting the y-axis so that thescanning positions after the coordinate transformation become uniform.Therefore, the function ft′(n) representing the scanning positions afterthe coordinate transformation satisfies the condition represented byExpression (15).ft′(n)=n  Expression (15)

Expression (15) means that, for example, a pixel position y′ (=ft′(2))in the sub-scanning direction after the coordinate transformationbecomes 2 with respect to the pixel number 2.

The broken lines connecting FIG. 10A and FIG. 10B to each otherrepresent the correspondence from an original coordinate position of they-axis to a coordinate position of the y′-axis after the coordinatetransformation from the left to the right, and indicate a state in whicha lower half (corresponding to n≤2) of the y-axis expands, and an upperhalf (corresponding to n≥2) contracts before and after the coordinatetransformation. A procedure for determining a coordinate after thecoordinate transformation of each pixel of input image data through thecoordinate transformation of FIG. 10A and FIG. 10B will be describedwith reference to FIG. 10C and FIG. 10D. In the same manner as in FIG.10A and FIG. 10B, the horizontal axis in FIG. 10C and FIG. 10Drepresents the pixel number “n”, and the vertical axis “y” (or y′)represents scanning positions in the sub-scanning direction. FIG. 10C isan illustration before the coordinate transformation, and FIG. 10D is anillustration after the coordinate transformation. A relationship betweenthe pixel number “n” and the coordinate position “y” of the input imagedata will be described below. First, the broken line of FIG. 10Crepresents a function fs(n) representing ideal scanning positions beforethe coordinate transformation and is represented by Expression (16).y=fs(n)  Expression (16)

Further, in the embodiment, the interval between the pixels in thesub-scanning direction of the input image data is uniform, and hence thefunction fs(n) is represented by Expression (17).fs(n)=n  Expression (17)

A scanning position of the y′-coordinate after the coordinatetransformation of a pixel number of interest “ns” of the input imagedata is determined through three steps described below. In the firststep, when the y-coordinate of an ideal scanning position correspondingto the pixel number “ns” of the input image data is defined as “ys”,“ys” can be determined by Expression (18).ys=fs(ns)  Expression (18)

A pixel number “nt” in which the scanning position before the coordinatetransformation is the same on the photosensitive drum 102 (solid line)is determined ((1) of FIG. 10C). The scanning position on thephotosensitive drum 102 is represented by the function y=ft(n), and arelationship of ys=ft(nt) holds. When an inverse function of thefunction ft(n) is defined as ft⁻¹(y), the pixel number “nt” isrepresented by Expression (19).nt=ft ⁻¹(ys)  Expression(19)

In the second step, the y′-coordinate after the coordinatetransformation (defined as “yt”) corresponding to the pixel number “nt”of the scanning position on the photosensitive drum 102 is determined byExpression (20) with the use of the function ft′(n) after the coordinatetransformation ((3) of FIG. 10D).yt=ft′(nt)  Expression (20)

The pixel number “ns” holds even when any number is selected, and hencean expression for determining the position “yt” of the y′-coordinateafter the coordinate transformation based on the pixel number “ns”corresponds to the function fs′(n) for determining the y′-coordinate bycalculation based on the pixel number “n” of the input image data. Thus,a general expression represented by Expression (21) is derived fromExpressions (18) to (20). A function indicating the ideal scanningposition represented by the broken line after the coordinatetransformation is represented by y′=fs′(n) ((3) of FIG. 10D).

yt=fs′(ns)=ft′(nt)=ft′(ft⁻¹ (ys))=ft′(ft⁻¹(fs(ns))) “ns” is generalizedinto “n” to obtain Expression (21).fs′(n)=ft′(ft ⁻¹(fs(n)))  Expression (21)

Further, Expression (17) and Expression (15) in which the pixel intervalof the input image data and the interval of the scanning positions afterthe coordinate transformation are set to be uniform, with the distanceof 1, are substituted into Expression (21). Then, Expression (21) isrepresented by Expression (22) with the use of the inverse functionft⁻¹(n) of the function ft(n) for deriving the scanning position fromthe pixel number “n”.fs′(n)=ft ⁻¹(n)  Expression (22)

Expression (8) in which the scanning positions are shifted uniformly inthe advance direction and the return direction as illustrated in FIG. 9Aand FIG. 9B, and Expression (11) for determining a position after thecoordinate transformation of the input image data also have an inversefunction relationship, and it can be confirmed that Expression (22)holds. Further, when applied to the case in which the dense or sparsestate of the scanning positions occurs as illustrated in FIG. 11A andFIG. 11B, the function “y” representing scanning positions before thecoordinate transformation is represented by Expression (23) when thefunction “y” is a straight line with a gradient “k”, passing through(n0, y0).fs(n)=y=k×(n−n0)+y0  Expression (23)

In order to determine a pixel position after the coordinatetransformation of the y-axis of the input image data, it is onlynecessary that an inverse function ((1/k)x(y−y0)+n0) be determined byExpressions (21) and (22), and the pixel number “n” be substituted intothe inverse function, and hence Expression (24) is derived.y′=(1/k)×(n−y0)+n0  Expression (24)

When the intervals between the scanning lines illustrated in FIG. 11Aare dense, and the intervals between the scanning lines illustrated inFIG. 11B are sparse, the positions of the scanning lines on thephotosensitive drum 102 after the coordinate transformation can berepresented by Expression (24) in both the cases. Further, a correctionvalue Cn of the pixel number “n” in the sub-scanning direction isdetermined by Cn=fs′(n)−fs(n).

Specifically in FIG. 11A, n0=y0=3 and k=0.8 are satisfied, andExpression (25) is obtained.fs′(n)=(1/0.8)×(n−3)+3  Expression (25)

For example, in the pixel number 3, fs′(3)=3.00 is satisfied, and thecorrection value C3 is 0.00 (=3.00-3.00). Further, in the pixel number5, fs′(5)=5.50 is satisfied, and the correction value C5 is +0.50(=+5.50−5.00). The correction values C1 to C5 when the scanningpositions are dense are illustrated in FIG. 13C.

Further, in FIG. 11B, n0=y0=3, and k=1.2 are satisfied, and Expression(26) is obtained.fs′(n)=(1/1.2)×(n−3)+3  Expression (26)

For example, in the pixel number 3, fs′(3)=3.000 is satisfied, and thecorrection value C3 is 0.000 (=3.000−3.000). Further, in the pixelnumber 5, fs′(5)=4.667 is satisfied, and the correction value C5 is−0.333 (=4.667−5.000). The correction values C1 to C5 when the scanningpositions are sparse are illustrated in FIG. 13D.

Further, even when a dense or sparse state and a shift are mixed in thescanning lines, an ideal scanning position after the coordinatetransformation can be determined with the use of Expression (21) or(22). The correction value setting portion 506 is configured to subjectan ideal scanning position to the coordinate transformation based on apositional deviation amount to determine the correction value CnN, andoutput information on the correction value CnN to the filter coefficientsetting portion 504.

(Filtering)

In the embodiment, the filtering is performed in order to generatecorrection data. In the embodiment, the filtering portion 501 isconfigured to perform the filtering through a convolution operationbased on the following filter function. That is, the filtering portion501 performs the filtering based on a positional relationship betweenthe pixel positions in the sub-scanning direction of pixels obtained bycorrecting scanning positions in the sub-scanning direction of pixels ofthe input image data, and positions of pixels in the sub-scanningdirection having an interval between scanning lines transformeduniformly by the coordinate transformation. A pixel before the filteringis also referred to as an input pixel, and a pixel after the filteringis also referred to as an output pixel. Further, a pixel before thefiltering is a pixel subjected to the above-mentioned coordinatetransformation.

The convolution function according to the embodiment can be selectedfrom linear interpolation illustrated in FIG. 12A, and bicubicinterpolation illustrated in FIG. 12B and FIG. 12C. The filter functionoutput portion 505 outputs information on the convolution function usedin the filtering to the filter coefficient setting portion 504 asinformation of the table, for example. In FIG. 12A to FIG. 12D, thevertical axis “y” represents a position in the sub-scanning direction,with a unit being a pixel, and a horizontal axis “k” represents amagnitude of a coefficient. Although the unit of the vertical axis “y”is set to a pixel, a line may be used as a unit because the sub-scanningdirection is illustrated.

The expression of FIG. 12A is represented by Expression (27).k=y+1(−1≤y≤0)k=−y+1(0<y≤1)0(y<−1,y>1)  Expression (27)

Expressions of FIG. 12B and FIG. 12C are represented by the followingtwo expressions.

$\begin{matrix}{{{bicubic}(t)} = \left\{ \begin{matrix}{{\left( {a + 2} \right){t}^{3}} - {\left( {a + 3} \right){t}^{2}} + 1} & \left( {{t} \leq 1} \right) \\{{a{t}^{3}} - {5a{t}^{2}} + {8a{t}} - {4a}} & \left( {1 < {t} \leq 2} \right) \\0 & \left( {2 < {t}} \right)\end{matrix} \right.} & {{Expression}\mspace{14mu}(28)} \\{\mspace{79mu}{k = {{{bicubic}\left( \frac{y}{w} \right)}/w}}} & {{Expression}\mspace{14mu}(29)}\end{matrix}$

In the embodiment, a is set to −1, and “w” is set to 1 in FIG. 12B andset to 1.5 in FIG. 12C, but “a” and “w” may be adjusted in accordancewith the electrophotographic characteristics of each image formingapparatus. The filter coefficient setting portion 504 is configured tooutput a coefficient (“k” described later) to be used in the filteringto the filtering portion 501 based on the information on the filterfunction obtained from the filter function output portion 505 and theinformation on the correction value C output from the correction valuesetting portion 506.

Now, description is given with reference to FIG. 12D. In FIG. 12D, thehorizontal axis represents a coefficient “k” to be used in thefiltering, and the vertical axis represents a position “y” in thesub-scanning direction. When the filtering portion 501 receives thecorrection value CnN from the correction value setting portion 506, thefiltering portion 501 determines a coefficient “kn” corresponding to thecorrection value CnN with the use of the filter function input from thefilter function output portion 505. White circles of FIG. 12D representcoefficients before the coordinate transformation. Further, in FIG. 12D,it is illustrated that coefficients k1 and k2 were set with respect to acorrection value C1N and a correction value C2N, respectively, ascoefficients “kn” to be used in the filtering (black circles). In theembodiment, the same convolution function is applied irrespective ofwhether the input image data is dense or sparse, and sampling isperformed at an ideal scanning position, to thereby store density perpredetermined area of the input image data.

(Specific Example of Filtering)

A specific example of performing the filtering with the use of theconvolution operation with a filter function by linear interpolation ofExpression (27) based on a coordinate position after the coordinatetransformation of the embodiment will be described with reference toFIG. 13A, FIG. 13B, FIG. 13C, and FIG. 13D. The filtering using theconvolution operation is performed by the filtering portion 501. FIG.13A to FIG. 13D correspond to FIG. 8A to FIG. 8D, respectively. Eachcolumn on the left side of FIG. 13A to FIG. 13D represents input pixelsafter the above-mentioned coordinate transformation. Further, eachcolumn on the right side of FIG. 13A to FIG. 13D represents scanningpositions on the photosensitive drum 102 after the above-mentionedcoordinate transformation. That is, the scanning positions in eachcolumn on the right side of FIG. 13A to FIG. 13D have been subjected tothe coordinate transformation so as to have a uniform interval and adistance of 1.

More specifically, the scanning positions in the sub-scanning directionof input pixels after the coordinate transformation are represented by astraight line (y′=fs′(n)) indicated by the alternate long and short dashline of the graph after the coordinate transformation illustrated on theright side of FIG. 9A, FIG. 9B, FIG. 11A, and FIG. 11B. The scanningpositions on the photosensitive drum 102 after the coordinatetransformation are represented by a straight line (y′=fs′(n)) indicatedby the solid line of the graph after the coordinate transformationillustrated on the right side of FIG. 9A, FIG. 9B, FIG. 11A, and FIG.11B. For example, in FIG. 9A, the shift amount is +0.2 (=S), and hencefs′(n)=y−0.2=n−0.2 is satisfied after the coordinate transformation.

Further, in FIG. 13A to FIG. 13D, the magnitude of a pixel value, thatis, a density value is represented by shading of circles. Further,numbers in parentheses indicate numbers of scanning lines, and are thesame as the pixel numbers illustrated in FIG. 8A to FIG. 8D. In eachgraph at the center of FIG. 13A to FIG. 13D, the horizontal axisrepresents density, and the vertical axis represents a position in thesub-scanning direction. The convolution operation involves developingwaveforms W (W1 to W5 with respect to the pixels (1) to (5)) obtained bymultiplying the filter function based on each coordinate position of aninput image (FIG. 12A) by a pixel value, and adding the waveforms W bysuperimposing.

FIG. 13A will be described first. The pixels (1) and (5) represented bywhite circles have a density of 0, that is, a pixel value of 0.Therefore, W1 and W5 obtained by multiplying a filter function by apixel value are both 0. The pixels (2), (3), and (4) represented byblack circles have the same density, and the maximum values of thewaveforms W2, W3, and W4 are the same. Thus, the pixels (2), (3), and(4) each result in a waveform obtained by developing the filter functionbased on the pixel position of the input pixel. The result of theconvolution operation is a sum (ΣWn, n=1 to 5) of all the waveforms.

A pixel value of an output pixel is sampled at the scanning position onthe photosensitive drum 102 after the scanning position is subjected tothe coordinate transformation. Therefore, for example, the pixel value(1) corresponding to the scanning position on the photosensitive drum102 intersects with the waveform W2 at a point P0, and hence iscalculated to be density D1. Further, the pixel value (2) intersectswith the waveform W2 at a point P2 and the waveform W3 at a point P1,respectively, and hence is calculated to be density D1+D2. The pixelvalues (3) to (5) are subsequently determined in a similar manner. Thepixel value (5) does not intersect with any waveform, and hence thepixel value thereof is set to 0. Further, the result obtained bycalculating the pixel values (1) to (5) of FIG. 13B to FIG. 13D arerepresented by shading of pixels in each column on the right side.

The positional deviation of the input pixels is illustrated so as tocorrespond to each pixel on the vertical axis of FIG. 13A to FIG. 13D.The positional deviation amount represented by the vertical axis of FIG.13A to FIG. 13D is information on the positional deviation amountdetermined by an inverse function in accordance with the coordinatetransformation of the scanning positions in the sub-scanning directionof the pixels of the input image. For example, in the case of FIG. 13A,as described with reference to FIG. 9A, the correction amount C of thepositional deviation amount S of the scanning lines is −0.2. Further,for example, in the cases of FIG. 13C and FIG. 13D, the correctionamounts C are calculated with the use of Expressions (25) and (26),respectively.

FIG. 13A is an illustration of a state in which the scanning positionsof the scanning lines are shifted in the advance direction in thesub-scanning direction, but the centers of gravity of the pixel valuesare shifted in the return direction, and hence the positions of thecenters of gravity of the pixel values are corrected. FIG. 13B is anillustration of a state in which the scanning positions of the scanninglines are shifted in the return direction in the sub-scanning direction,but the centers of gravity of the pixel values are shifted in theadvance direction, and hence the positions of the centers of gravity ofthe pixel values are corrected. FIG. 13C is the case in which theintervals between the scanning positions are dense, and is anillustration of a state in which the distribution of density is wideneddue to the convolution operation after the coordinate transformation tocancel the local concentration of density, to thereby correct a localchange in density. Further, FIG. 13D is the case in which the intervalsbetween the scanning positions are sparse, and is an illustration of astate in which the distribution of density is narrowed due to theconvolution operation after the coordinate transformation to cancel thedispersion of density, to thereby correct a local change in density. Inparticular, the pixel value (3) of FIG. 13D is a density of (100+a) %which is higher than 100%.

(Filtering)

Referring back to FIG. 7, in S3604 of FIG. 7, the CPU 303 performs thefiltering with the filtering portion 501 based on the attributeinformation for correction generated in S3603. Specifically, the CPU 303performs a convolution operation and re-sampling with respect to theabove-mentioned input image. The processing of S3604 performed by theCPU 303 will be described below in detail with reference to theflowchart of FIG. 14. When the CPU 303 starts the filtering through theconvolution operation with the filtering portion 501, the CPU 303performs the processing in S3703 and subsequent steps.

In S3703, when the spread of the convolution function is defined as L,the CPU 303 extracts lines of an input image within a range of beforeand after ±L of the position in the sub-scanning direction of a line“yn” (position “yn”) of an output image of interest, that is, the rangeof a width of 2 L (range of from (yn−L) to (yn+L)). In this case, L isdefined as a minimum value at which the value of the convolutionfunction becomes 0 outside of the range of from +L to −L of theconvolution function. For example, in the linear interpolation of FIG.12A, L is equal to 1. In the bicubic interpolation of FIG. 12B, L isequal to 2. In the bicubic interpolation of FIG. 12C, L is equal to 3.The ymin and ymax within a range of from ymin to ymax of thecorresponding input image satisfy the following condition with the useof Expression (22).ft ⁻¹(ymin)=yn−L,ft ⁻¹(ymax)=yn+L  Expression (30)

When Expression (30) is modified, ymin and ymax are determined byExpression (31).ymin=ft(yn−L),ymax=ft(yn+L)  Expression (31)

Thus, the lines of the input image to be extracted with respect to theline “yn” of the output image of interest are lines of all the integerswithin a range of from ymin to ymax.

When the line of the output image of interest is denoted by “yn”, andthe line of the input image to be subjected to the convolution operationis denoted by “ym”, a distance “dnm” is represented by Expression (32).dnm=yn−ft ⁻¹(ym)  Expression (32)

Thus, in S3704, the CPU 303 obtains a coefficient “knm” as a convolutionfunction g(y) with the filter coefficient setting portion 504 byExpression (33).knm=g(dnm)  Expression (33)

In S3707, the CPU 303 obtains pixel data on the position n in thesub-scanning direction in the input image extracted in S3703 and theposition N of interest in the main scanning direction. The pixel data isdefined as input pixel data Pin_(m). In S3708, the CPU 303 performs theconvolution operation with the filtering portion 501, to thereby end theprocessing. More specifically, the filtering portion 501 subjects thecorresponding coefficient “knm” determined in S3704 and the input pixeldata Pin_(m) obtained in S3707 to a product-sum operation, to therebydetermine a value Pout_(n) of the pixel of interest. The input pixeldata Pin_(m) is density of the pixel of interest before the filtering,and the value Pout_(n) of the pixel of interest is output pixel data andis density of the pixel of interest after the filtering.

$\begin{matrix}{{Pout}_{n} = {\sum\limits_{m}^{all}{k_{nm} \cdot {Pin}_{m}}}} & {{Expression}\mspace{14mu}(34)}\end{matrix}$

Expression (34) corresponds to FIG. 13A to FIG. 13D. The darkness(density) of the circles on the left side in FIG. 13A to FIG. 13Dcorresponds to the input pixel data Pin_(m). D1 and D2 in FIG. 13Acorrespond to knm×Pin_(m). The darkness (density) of the circles on theright side in FIG. 13A to FIG. 13D corresponds to Pout_(n).

Thus, in the embodiment, distortion and uneven image density of an imagecaused by the deviation of an irradiation position due to a variation inarrangement intervals of light emitting points of a laser light sourceand the optical face tangle error of the mirror faces of the rotarypolygon mirror 204 are corrected as follows. First, a pixel position ofan input image is subjected to the coordinate transformation based on aprofile of positional deviation in the sub-scanning direction of theinput image. Then, the filtering and sampling are performed, therebybeing capable of cancelling positional deviation and local biaseddensity such as banding while maintaining the density of each inputimage, with the result that a satisfactory image can be obtained. In theembodiment, a positional deviation amount in the sub-scanning directioncan be calculated in consideration of different optical face tangleerrors of the rotary polygon mirror 204 in the main scanning direction.

First Embodiment

<Chart Output>

In the first embodiment, a user or a service person performs visualjudgement with the use of a test chart and inputs the above-mentionedamplitude gain Gb through a user interface. In the embodiment, a methodof determining the amplitude gain Gb for adjusting (correcting) abanding correction amount described in Expression (2) will be describedin detail.

FIG. 15D is an illustration of a test chart. Images (hereinafterreferred to as “patches”) for determining the amplitude gain Gb areformed on the surface of a sheet S of an A4 size. A total of 25 patchesare arranged on the sheet S so that 5 patches are arranged in thevertical direction (sub-scanning direction) and 5 patches are arrangedin the horizontal direction (main scanning direction). In this case, thepatches arranged in the main scanning direction are images having thesame amplitude gain Gb. The patches arranged in the sub-scanningdirection are images corresponding to image data subjected to filteringwith the use of different amplitude gains Gb.

FIG. 15A is a graph for showing the mirror faces A to E of the rotarypolygon mirror 204, that is, a phase of rotation of the rotary polygonmirror 204 in the horizontal axis, and an amount of optical face tangle(Am) of the mirror faces of the rotary polygon mirror 204 in thevertical axis. As shown in FIG. 15A, an amount of optical face tangle of0 to the maximum value thereof are set to an amplitude Am of a referenceprofile. The reference profile is a profile specific to each lightscanning device, and the amplitude Am is the above-mentioned amount ofoptical face tangle Ybm. In the embodiment, as described above, theamplitude Am (=Ybm) of the reference profile is stored in advance in thememory 302 of the light scanning device 104 at the time of factoryshipment or the like. FIG. 15B is an illustration of a part of thememory 302. The memory 302 stores the amplitude Am (=Ybm) of thereference profile of each of the mirror faces A to E of the rotarypolygon mirror 204, for each block obtained through the division in themain scanning direction for each mirror face.

The images of the patches formed on the sheet S are subjected tofiltering based on a profile obtained by multiplying the amplitude Am ofthe reference profile stored in the memory 302 by the amplitude gain Gb.As the image, a generally used screen image is used. An image in whichbanding caused by an optical face tangle error is visually recognizedeasily may be used.

The patches on the test chart are printed at positions corresponding tofive correction blocks (b=1 to 5 described above) obtained through thedivision in the main scanning direction. In this case, the fivecorrection blocks correspond to five blocks of one mirror face of therotary polygon mirror 204. The patches in the sub-scanning directioninclude the amplitude gain Gb corresponding to an upper limit value of afocus tolerance with the patch having the amplitude gain Gb of 0 beingthe center, and the amplitude gain Gb is gradually changed. Here, theupper limit value of the focus tolerance is represented by ±Xg, and anintermediate value from 0 to Xg is presented by ±Yg. (A) of FIG. 15Crepresents a profile (Am×(+Xg)) when the amplitude gain Gb is set to+Xg, and (B) of FIG. 15C represents a profile (Am×0) when the amplitudegain Gb is set to 0. (C) of FIG. 15C represents a profile (Am×(−Xg))when the amplitude gain Gb is set to −Xg. In each profile, thehorizontal axis represents a mirror face of the rotary polygon mirror204, and the vertical axis represents an amount of optical face tangle.

In the sub-scanning direction of the sheet S, the patches, which areformed by filtering, are arranged based on positional deviation amountscalculated with the use of the five amplitude gains Gb of +Xg, +Yg, 0,−Yg, and −Xg. An operation portion (not shown) of the image formingapparatus 100 includes an execution button configured to designateprinting execution of the above-mentioned test chart, and the user orthe service person can print the test chart by pressing the executionbutton at any timing.

After the test chart is printed, the user or the service person selectsa patch having banding in the smallest amount from the five patches inthe sub-scanning direction by visually inspecting the test chart or withthe use of an analysis device capable of mechanically analyzing theamount of banding. In other words, the user or the service personselects the amplitude gain Gb having banding in the smallest amount.Here, it is assumed that the user or the service person determines theamplitude gain Gb for each five blocks in the main scanning direction.For example, when a patch formed by correcting a block 1 with theamplitude gain Gb being set to “−Yg” has banding in the smallest amount,“−Yg” is selected as an amplitude gain G1 of the block 1. Further, forexample, when a patch formed by correcting a block 3 with the amplitudegain Gb being set to “+Xg” has banding in the smallest amount, “+Xg” isselected as an amplitude gain G3 of the block 3. Thus, the user or theservice person inputs, through the operation portion (not shown), avalue of the amplitude gain Gb (b=1 to 5) of a patch having the amountof banding reduced most, depending on the above-mentioned five blocksobtained through the division in the main scanning direction. After theamplitude gain Gb is selected with the use of the test chart asdescribed above, a positional deviation amount is determined byExpression (2) with the use of the selected amplitude gain Gb, andfiltering and the like are performed based on the determined positionaldeviation amount, to thereby correct the image data. As described above,in the embodiment, gain adjustment is performed with the use of theamplitude gain Gb selected with the use of the test chart, and bandingis corrected in accordance with focus deviation in the main scanningdirection specific to a main body of the image forming apparatus 100.

In the embodiment, uneven image density can be reduced even when focusdeviation of a laser beam radiated on a photosensitive member from alight scanning device occurs due to a variation on an image formingapparatus side and a mounting error of the light scanning device.

Second Embodiment

<Calculation of Optimum Gain Gb Based on Focus Distance Information>

In the second embodiment, a method involving storing in the memory 302focus distance information Δxb (b=1 to 5) measured in advance andcalculating an amplitude gain Gb for adjusting a banding correctionamount based on the focus distance information Δxb will be described.The focus distance information Δxb corresponds to a illustrated in FIG.17A. Parts having configurations different from those of the firstembodiment are described in detail, and the same configurations aredescribed with the use of the same reference symbols. Further, in theembodiment, in FIG. 1B, the image data is input to the CPU 303 but theamplitude gain Gb is not input thereto, and the configurations of thephotosensitive drum 102, the light scanning device 104, and a controlportion of the light scanning device 104 are the same as those of thefirst embodiment.

The distance from a mounting seat surface of the light scanning device104 of the image forming apparatus 100 to the surface of thephotosensitive drum 102 is measured in an assembly adjusting step of theimage forming apparatus 100 and information of the measured distance isstored in the memory 302 as the focus distance information Δxb. Thefocus distance information Δxb contains pieces of data separatelycorresponding to the blocks 1 to 5 obtained through the division in themain scanning direction.

An address map storing the focus distance information Δxb is shown inTable 2. In the same manner as in Table 1 of the first embodiment,position information of a laser beam and face information are alsostored in the address map of Table 2. Addresses 1 to 32 are the same asthose of Table 1, and hence description thereof is omitted. In addresses33 to 37 of the memory 302, focus distance information Δx1 to Δx5 arestored so as to correspond to the five blocks in the main scanningdirection.

TABLE 2 Address Data 1 LD2 position information X1 2 LD3 positioninformation X2 3 LD4 position information X3 4 LD5 position informationX4 5 LD6 position information X5 6 LD7 position information X6 7 LD8position information X7 8 Face A position information Y1A 9 Face Aposition information Y2A 10 Face A position information Y3A 11 Face Aposition information Y4A 12 Face A position information Y5A 13 Face Bposition information Y1B 14 Face B position information Y2B 15 Face Bposition information Y3B 16 Face B position information Y4B 17 Face Bposition information Y5B 18 Face C position information Y1C 19 Face Cposition information Y2C 20 Face C position information Y3C 21 Face Cposition information Y4C 22 Face C position information Y5C 23 Face Dposition information Y1D 24 Face D position information Y2D 25 Face Dposition information Y3D 26 Face D position information Y4D 27 Face Dposition information Y5D 28 Face E position information Y1E 29 Face Eposition information Y2E 30 Face E position information Y3E 31 Face Eposition information Y4E 32 Face E position information Y5E 33 Focusdistance information Δ × 1 34 Focus distance information Δ × 2 35 Focusdistance information Δ × 3 36 Focus distance information Δ × 4 37 Focusdistance information Δ × 5

The CPU 303 reads the focus distance information Δxb from the memory 302and calculates the amplitude gain Gb described later.

FIG. 16C is a graph for showing a relationship between the focusdistance information Δxb (hereinafter referred to as “focus distanceerror”) and the amplitude gain Gb. FIG. 16C is a graph for showing thefocus distance error Δxb in the horizontal axis and the amplitude gainGb in the vertical axis. As described above, the amplitude gain Gbchanges depending on the focus distance error Δxb(a) which is also afocus deviation amount. Specifically, when the focus distance error Δxbincreases, the amplitude gain Gb also increases. Further, FIG. 16A andFIG. 16B are each a graph for showing a mirror face of the rotarypolygon mirror 204 in the horizontal axis and an amount of optical facetangle in the vertical axis. As shown in FIG. 16A and FIG. 16B, theamount of optical face tangle changes depending on the amplitude gainGb. Specifically, when the amplitude gain Gb increases, the amount ofoptical face tangle also increases. As a result, when the focus distanceerror Δxb which is a focus deviation amount increases, the amount ofoptical face tangle also increases. In this case, the focus deviationamount and the amount of optical face tangle are uniquely determined byoptical characteristics of a light scanning device. A function of thefocus distance error Δxb and the amplitude gain Gb shown in FIG. 16C isfor showing a relationship between the focus distance error Δxb and theamplitude gain Gb in a simplified manner for the purpose ofsimplification of description, and is represented by, for example, alinear function. Depending on the optical design condition, the opticalscanning device may have non-linear characteristics. The above-mentionedfunction is determined based on a design value determined in opticaldesign.

A function of the focus distance error Δxb and the amplitude gain Gb inthe embodiment is represented by a linear function of a gradient R. InExpression (35), the amplitude gain Gb is determined with the use of thegradient R.Gb=Δxb×R  Expression (35)

-   -   (b=1 to 5)

As described above, when the focus distance error (focus deviationamount) increases, the amount of optical face tangle also increases.Therefore, it is understood from Expression (35) that, when the amountof optical face tangle increases, the amplitude gain Gb also increases.As shown in FIG. 16A, when the optical face tangle error is small, theamplitude gain is also small. As shown in FIG. 16B, when the amount ofoptical face tangle increases, the amplitude gain also increases. Thesubsequent processing, specifically, the calculation of a positionaldeviation amount with the use of the amplitude gain Gb, the filteringwith the use of a positional deviation amount, and the like areperformed in the same manner as in the first embodiment, and descriptionthereof is omitted.

Through the above-mentioned operations, in the embodiment, the amplitudegain Gb can be calculated to calculate the amount of optical face tanglein the main body of the image forming apparatus 100 without using thetest chart. A variation in each image forming apparatus can be addressedby holding the focus distance information (focus position deviation) Δxbof the image forming apparatus 100 in the memory 302. Therefore, evenwhen a light scanning device is replaced for maintenance or the like,correction can be made with an optimum banding correction amount withoutperforming a special operation.

As described above, in the embodiment, uneven image density can bereduced even when focus deviation of a laser beam radiated on aphotosensitive member from a light scanning device occurs due to avariation on an image forming apparatus side and a mounting error of thelight scanning device.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2016-011258, filed Jan. 25, 2016, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. An image forming apparatus, comprising: a lightsource comprising a plurality of light emitting points; a photosensitivemember configured to rotate in a first direction so that a latent imageis formed on the photosensitive member by light beams emitted from thelight source; a deflection unit configured to deflect the light beamsemitted from the light source with a mirror face and cause light spotsof the light beams radiated on the photosensitive member to be moved ina second direction orthogonal to the first direction to form scanninglines; a storage unit configured to store information on positionaldeviation of the plurality of light emitting points in the firstdirection and information on an optical face tangle error of the mirrorface of the deflection unit in accordance with the second direction; acorrection unit configured to correct the information on the opticalface tangle error stored in the storage unit, based on a deviationamount from a predetermined distance between the deflection unit and thephotosensitive member; a calculation unit configured to calculate apositional deviation amount based on the information on the positionaldeviation stored in the storage unit and the information on the opticalface tangle error corrected by the correction unit; a transformationunit configured to transform a position of a pixel of an input image byperforming coordinate transformation based on the positional deviationamount calculated by the calculation unit so that an interval betweenthe scanning lines on the photosensitive member becomes a predeterminedinterval; and a filtering unit configured to obtain a pixel value of apixel of an output image by subjecting a pixel value of the pixel of theinput image to a convolution operation based on the position of thepixel of the input image after the coordinate transformation.
 2. Animage forming apparatus according to claim 1, wherein the storage unitdivides the mirror face of the deflection unit into a predeterminednumber of blocks in the second direction and stores the information onthe optical face tangle error for each of the divided blocks.
 3. Animage forming apparatus according to claim 2, further comprising: animage forming unit configured to form an image on a recording medium;and a setting unit configured to set a gain for correcting theinformation on the optical face tangle error stored in the storage unitbased on the deviation amount from the predetermined distance, whereinthe setting unit causes the image forming unit to form a plurality ofimages each having a different gain on the recording medium in the firstdirection, and sets a gain corresponding to an image selected from theplurality of images for each of the blocks.
 4. An image formingapparatus according to claim 2, wherein the storage unit storesinformation on the deviation amount from the predetermined distance foreach of the blocks in advance, and wherein the calculation unitcalculates a gain for correcting the information on the optical facetangle error based on the information on the deviation amount from thepredetermined distance stored in the storage unit.
 5. An image formingapparatus according to claim 4, wherein the filtering unit performs theconvolution operation with use of linear interpolation or bicubicinterpolation.
 6. An image forming apparatus according to claim 4,wherein the pixel value comprises a density value, and wherein a densityvalue per predetermined area is stored before and after the filteringunit performs the convolution operation.
 7. An image forming apparatusaccording to claim 4, wherein the filtering unit obtains, when a widthin the first direction within a range excluding 0 of a convolutionfunction to be used for the convolution operation is defined as 2 L, arange of from ymin to ymax of pixels of the input image corresponding toa range of the width of 2 L with a position “yn” of a predeterminedpixel of the output image being a center as the following expressions:ymin=ft(yn−L); andymax=ft(yn+L).
 8. An image forming apparatus according to claim 1,wherein the transformation unit obtains the position of the pixel of theinput image after the coordinate transformation with use of an inversefunction ft⁻¹(n) of a function ft(n) by the following expression:fs′(n)=ft′(ft ⁻¹(fs(n))) where: fs(n) represents a function indicating aposition of an n-th pixel in the first direction of the input image;ft(n) represents a function indicating a position of the n-th pixel inthe first direction of the output image; fs′(n) represents a functionindicating a position of the n-th pixel in the first direction of theinput image after the coordinate transformation; and ft′(n) represents afunction indicating a position of the n-th pixel in the first directionof the output image after the coordinate transformation.
 9. An imageforming apparatus according to claim 5, wherein the transformation unitobtains, when the function fs(n) satisfies fs(n)=n and the functionft′(n) satisfies ft′(n)=n, the position of the pixel of the input imageafter the coordinate transformation by the following expression:fs′(n)=ft ⁻¹(n).
 10. An image forming apparatus according to claim 1,wherein the predetermined interval is determined in accordance with aresolution of image formation by the image forming apparatus.